What is Rotation: Definition and 1000 Discussions

A rotation is a circular movement of an object around a center (or point) of rotation. The geometric plane along which the rotation occurs is called the rotation plane, and the imaginary line extending from the center and perpendicular to the rotation plane is called the rotation axis ( AK-seez). A three-dimensional object can always be rotated about an infinite number of rotation axes.
If the rotation axis passes internally through the body's own center of mass, then the body is said to be autorotating or spinning, and the surface intersection of the axis can be called a pole. A rotation around a completely external axis, e.g. the planet Earth around the Sun, is called revolving or orbiting, typically when it is produced by gravity, and the ends of the rotation axis can be called the orbital poles.

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  1. E

    Rotating spool on table with friction

    Homework Statement I am referring to this thread and question: https://www.physicsforums.com/threads/rotation-of-a-spool-about-rough-ground.295666/ Here is the problem, restated: Homework Equations ##\tau_{net} = I\alpha## ##\tau = Frsin(\theta)## ##F_{net} = Ma_{cm}## ##\alpha = a_{cm} /...
  2. C

    Understanding Rotational Velocity and Its Significance in Physics

    As a student taking my first step into rotational physics in a classroom filled with students who have a year of this ahead of me I beg for help! :P So what is Rotational velocity? What does it define? How do signs work with rotation? What does its acceleration mean? Angular Velocity is...
  3. E

    Torque on Rod Due to Normal Force at a Hinge

    Homework Statement In this diagram, I wondered if there is any torque due to the normal force from the hinge, once the support stick is removed. I also want to know what the normal force would be at the hinge. The cup and ball are to be ignored here (essentially massless). Homework Equations...
  4. W

    B The bizarre rotation of galaxies

    The planets rotate around our sun faster and faster the closer they are.The Suns rotate around a black hole in a galaxy as if they were a record on a record player.Gravitational laws as we understand them don't seem to apply.Is it possible that a black holes gravitational pull not only freezes...
  5. ang__

    How Do You Calculate the Total Inertia Matrix for a Composite Object?

    Homework Statement The object is made out of multiple parts. The inertia matrices of every part are given. Only one part is rotating. How do I find the total inertia matrix. Homework EquationsThe Attempt at a Solution I thought that I could sum the inertia matrices, after tranforming them to...
  6. C

    Rotation of a hoop about an off-center axis

    Homework Statement I am studying for a test and am struggling with this question on the practice exam. The answer is 9.9 I am not sure how she got to the answer though A hoop of mass 300 g. and a radius of 20 cm rotates about an axle at the edge of a hoop. The hoop starts at highest...
  7. Jamie_Pi

    Blocks falling while attatched to pulley

    Homework Statement The two blocks, m1 = 3.3 kg and m2 = 4.8, in the figure below are connected by a massless rope that passes over a pulley. The pulley is 12 cm in diameter and has a mass of 2.0 kg. As the pulley turns, friction at the axle exerts a torque of magnitude 0.64 N · m. If the blocks...
  8. K

    Maths required for rotation point

    Hi The first thing to say about this is that I don’t have a clue where to start. What I’m looking for is somewhere (maybe a website or just a brief introduction) I can study – and learn – about the forces involved and the maths required. _______ Say I have an item/length/beam/weight/etc (C...
  9. H

    Linear movement vs rotation

    Hi, The goal here is to increase/decrease the angle x by 5 degrees. the black circles represent a rubber tire (same as car tires, only smaller), 5cm in diameter, rotating on it's center, powered by a motor. each wheel has 40 psi (2.76 bar) of air in it. the yellow tray on both diagrams are...
  10. Alexanddros81

    A package of mass m is placed inside a drum

    Homework Statement 13.69 A packege of mass m is placed inside a drum that rotates in the vertical plane at the constant angular speed ##\dot {θ} = 1.36 rad/s##. If the package reaches the position θ = 45deg before slipping, determine the static coefficient of friction between the package and...
  11. A

    What is the angular acceleration of the rod?

    Homework Statement A thin, uniform, 18.5 kg post, 2.10 m long, is held vertically using a cable and is attached to a 5.00 kg mass and a pivot at its bottom end (as shown below). The string attached to the 5.00 kg mass passes over a massless, frictionless pulley and pulls perpendicular to the...
  12. A

    Number of rotation till the drum comes rest

    Homework Statement A solid cylinder rotates till it comes to rest. It has inititial angular velocity. To stop the drum a mass m ishung the belt which has a friction coefficient with the drum material as u we have to find no of rotationd all the data is known and correct Homework Equations...
  13. Q

    I Coordinate transformation - Rotation

    How author derives these old basis unit vectors in terms of new basis vectors ? Please don't explain in two words. \hat{e}_x = cos(\varphi)\hat{e}'_x - sin(\varphi)\hat{e}'_y \hat{e}_y = sin(\varphi)\hat{e}'_x + cos(\varphi)\hat{e}'_y
  14. Alfredo Tifi

    B Relative Rotation: Physics Approach for Newton's Bucket in Empty Universe

    Is there any physics approach useful to establish what should happen to a Newton's water bucketful rotating in a hypothetically empty universe (but for the bucket)? What the bucket would be rotating respect to in that one-bucket-universe? Everything rotating seems to have absolute (not relative)...
  15. redtree

    I Galaxy Rotation Curves and Mass Discrepancy

    I apologize for the simple question, but I am trying to understand the Mass Discrepancy-Acceleration Relation and its relationship to ##\mu(x)## (from https://arxiv.org/pdf/astro-ph/0403610.pdf). The mass discrepancy, defined as the ratio of the gradients of the total to baryonic...
  16. JTC

    I Left translate back to I in SO(3)

    Hello I am hoping someone can explain a sentence to me. Unfortunately, I do not even recall where I read it. I wrote it down years ago and long since lost the source. (Now I think some of it is making sense, but I don't remember the source.) Consider R(t) as an orthogonal rotation matrix...
  17. Z

    Rotation Operator: Interaction between Two-Level Atom in {|g>, |e>} Basis

    Hi, I'm working on the interaction between a two level atom (|g>, |e>) In my exercise we have to use the rotation operator : R(t)=exp[i(σz+1)ωt/2] with σz the pauli matrix which is in the {|g>,|e>} basis : (1 0) (0 -1) If i want to represent my rotation operator in the {|g>,|e>} basis. Then...
  18. K

    Relationship between translation and rotation

    Homework Statement Prove or disprove: Every translation is a product of two non-involutory rotations. Homework EquationsThe Attempt at a Solution :[/B] I am not sure if I got the right proof for the special situation: A translation is the product of two reflections with parallel reflections...
  19. E

    Door Rotation: The Influence of Attached Rods and Forces

    If I were to put attach a long rod to the side of a door (the exact opposite of the side where it is hinged, the slim part) And then I apply a force to the the right side of the rod I attached, would the door rotate to the right, or would the hinge completely oppose the force and the door...
  20. E

    Why do we fall forward when walking and rotating?

    When we push off with with our foot on the ground and accelerate, why do we fall forward and catch ourselves with our swinging leg, while when push forward the inertia of our body must actually tilt it backwards, how do we fall to the front?
  21. arpon

    Two successive rotation (Goldstein problem 4.13)

    Homework Statement Suppose two successive coordinate rotations through angles ##\Phi_1## and ##\Phi_2## are carried out, equivalent to a single rotation through an angle ##\Phi##. Show that ##\Phi_1##, ##\Phi_2## and ##\Phi## can be considered as the sides of a spherical triangle with the angle...
  22. E

    Me, A Rod and A Table With Little Friction

    Lets say I have a massive rod laying on a table with little froction, screwed into the table on one side to become our pivot point, and I lay next to it with my feet pointing towards the rod. First scenario: I position myself very close to the pivot point and push, the rod rotates and I move...
  23. saadhusayn

    I Matrix for transforming vector components under rotation

    Say we have a matrix L that maps vector components from an unprimed basis to a rotated primed basis according to the rule x'_{i} = L_{ij} x_{j}. x'_i is the ith component in the primed basis and x_{j} the j th component in the original unprimed basis. Now x'_{i} = \overline{e}'_i. \overline{x} =...
  24. kostoglotov

    Viscous drag parallel to the axis of rotation: Control Systems

    Homework Statement https://i.imgur.com/WPAKuf4.png seeking G(s) = \frac{\theta_2(s)}{\tau(s)} Homework EquationsThe Attempt at a Solution What does it mean when the viscous drag is parallel to the axis of rotation?[/B] It also turns out that this system needs two equations. I can sort...
  25. arpon

    I Experiment: Spin Rotation Operator

    How do we experimentally apply the operator ## \exp{\left(-i\phi\frac{ S_z}{\hbar}\right)}## on a quantum mechanical system? (Here ##S_z## is the spin angular momentum operator along the z-axis) For example, on a beam of electrons?
  26. D

    How to explain the phenomenon of optical rotation of chiral?

    I am Professor of Inorganic Chemistry of the State University of Southwest of Bahia - UESB. I have a PhD from UFMG in Natural Product Chemistry. I use the polarimeter in my experiments and would like to understand what happens on a micro scale (chiral molecules) to provide the phenomenon of...
  27. J

    Change in a vector upon rotation of the coordinate frame

    Homework Statement Hi everyone. We were discussing conservation of angular momentum as a consequence of rotational invariance in class. There was one point where we needed to compute the change in a vector A when the coordinate frame is rotated by angle Δ(Φ). Homework Equations The teacher...
  28. L

    B Exploring Rotation Matrices: Intuitive Insights and Geometric Interpretation

    Can anyone give me geometric and intuitive insight on Rotation matrices which has two sets of coordinates after Transformation?
  29. G

    Moment of inertia changes during rotation -- Calculate work?

    Hi everyone, i have a question Moment of inertia changes during rotation. Calculate the work that changes kinetic energy? Angular moment (along the axis of rotation) L = I * w A point mass M rotates along an axis attached to a mass-negligible rod, of length r. If someone moves the mass M at...
  30. I

    Rotation w/constant angular acceleration

    Homework Statement A flywheel turns through 40 rev as it slows from an angular speed of 1.5 rad/s to a stop. (a) Assuming a constant angular acceleration, find the time for it to come to rest. (b) What is its angular acceleration? (c) How much time is required for it to complete the first 20 of...
  31. redtree

    I Galaxy Rotation Curves: Newton's Shell Theorem Impact

    I apologize for the simple question, but I have not been able to find the answer. For the inner portion of a galaxy rotation curve (where the outer portion is the part invariant to distance and the inner part is where rotational velocity increases with radius), how much is simply due to...
  32. Y

    Calculate torque of an 80kg object rotating on its central axis

    Hello, I have a setup whereby: 1) A circular plate with fillet under-edge, is sitting like a bowl on some ball bearings. Imagine if you will a bowl sitting in a way that it can rotate and move a bit up and down etc. without much friction. 2) The plate needs to rotate at about 4 or 5 rpm. 3) The...
  33. B

    Rotation problem - AP Physics 1

    Hey guys, I'm having trouble understanding this problem that was on an AP Physics 1 sample questions page: So a couple of questions here: (By the way, I know the answer is C) 1. My teacher explained that the net torque here on the assembly would be zero(will ask him again later). Is this...
  34. B

    Choosing Axis of Rotation in Cylinder Oscillation Problem

    Homework Statement Here is a problem we worked in class. I already know the answer, just had a question on the method. Two cylinders are connected with by a small rod (with presumably negligent mass) through their centers. The cylinders can roll freely. A spring is attached to the small rod...
  35. O

    Angular Acceleration of a Pulley with Mass

    Homework Statement A pulley hangs of mass, m, and radius, R, hangs from the ceiling. Two blocks of masses, m1 and m2 are connected by a massless, non-stretchable rope on the pulley (assume no slipping). What is the angular acceleration of the pulley and what is the ratio of the tension forces...
  36. Sirsh

    Measuring relative rotation of node - ANSYS WorkBench

    Hi all, I have a rather trivial issue I am trying to solve, but it seems like there isn't anything available online that I can find to help me. For this question, imagine I have a 2D annulus with a fixed inner ring and frictionless outer ring. I apply a moment to the outer ring and create...
  37. J

    Find the tension in the lower string and the rotation rate

    Homework Statement A 700g ball rotates around a vertical shaft supported by two strings. If the tension in the upper string is 20.0 N, determine (I have attached the file) a. The tension in the lower string. b. The rotation rate in rpm of the system. Homework Equations [/B] F=ma F= m...
  38. B

    Torque of Pulley with Two Masses2

    Homework Statement Two weights are connected by a very light flexible cord that passes over a 40.0-N frictionless pulley of radius 0.300 m. Weight #1 is 125 N and Weight #2 is 75 N. The pulley is a solid uniform disk and is supported by a hook connected to the ceiling. What force does the...
  39. C

    Why don't we feel the Earth's rotation?

    Pardon me if this seems like an incredibly naive question. Perhaps the question could also be rephrased as such: "Why do the laws of classical mechanics hold true with Earth as a frame of reference?" A quick google search turned up the usual answer: the Earth rotates at a constant speed...
  40. peroAlex

    Induced Voltage of Rotating Circular Loop

    HI! I'm a student, this question appeared in one of the old tests. I though I had it solved but apparently I must have missed somewhere. Could someone please at least hint me where I went wrong? Homework Statement Thin wire is wound into circular frame with radius ## r = 0.05m ## which...
  41. C

    Solving a Rolling Coin Problem: Is it 3 or 4?

    Homework Statement A coin of radius R rolls around a coin of radius 3R which is fixed.If the coin rolls without slipping, How many times does the coin rotates around its axis ? Homework Equations Xpm=RΘ for non slipping The Attempt at a Solution The center of mass moves a distance of...
  42. G

    Rotational Torque/Force Problem (rod around hinge)

    Homework Statement A Rod of Mass "M" is attached to a two-way hinge on the floor. It is being pulled by a spring (extension spring, so force is pulling the rod to the right, causing it to move clockwise). The hinge is frictionless. the rod has a mass of 5kg evenly distributed the pulling...
  43. D

    A Principal axis of rotation

    I have a body in 3D-space and I would like to calculate the rotation axis when the body moves from A to B. I know the location (x, y and z) and the orientation (rx, ry and rz (axis angles)) at both A and B. The difference between A and B is small. The time instant during a dynamics simulation...
  44. P

    Rotation vs Translation for elbow joint

    If I were to cut the string and let the board move, I know I would get rotation. But, since the center of mass of the beam is moving as well (in a circle) could I also say that the board is translating once the string is cut?
  45. Ricky Lalduhzuala

    B Feeling Earth's Rotation: A Teleported Alien's Perspective

    If someone from the outer space suddenly teleport to the Earth , will it feel the rotation of the earth? will it be disturbed by the fast rotating earth.
  46. M

    MHB Rotation around an arbitrary point

    Hey! :o I want to rotate the point $(10, 11)$ with rotation angle $\frac{\pi}{3}$ around the point $P=(-1,-1)$. I have done the following: We translate about $-\vec{OP}$: \begin{equation*}P'=(-1\mid -1)-(-1\mid -1)=(0\mid 0)\end{equation*} We rotate around the origin...
  47. G

    Eddy current losses in microelectric generators?

    For a microscale electric generator (where the driving force is a fraction of a Newton), can losses from eddy currents be significant enough to noticeably alter the rotational velocity of the rotor? Because my understanding is that the rotation is basically taken as a constant when examining the...
  48. I

    What is the calculation for the angle formed by the rotated x-axis in a 3D plot?

    Homework Statement I am working in Matlab, and have a 3D plot that I made: x is parallel to axis labeled "lateral direction (m)" y is parallel to axis labeled "long. dir. (m)" z is normal to these (right hand coordinate sytem) The original view was looking parallel with +y. To get the...
  49. M

    Where Can I Find an Affordable One-Way Rotation Mechanism?

    Does anyone know if the following is available as an off-the-shelf component and what would it be called? One-way rotation mechanism Has detents or stops at specified intervals (such as every 90 degrees) Fairly small - for attaching an approximately 2" diameter wheel or circular disc to Doesn't...
  50. A

    Is my Cyclette Generating Enough Power at Resistance Level 4?

    Hi all! I have a cyclette with 8 resistance levels set magnetically using a knob (a magnet is moved near the rotating disk thereby increasing its rotating resistance). The distance from the pedal to the center is 0.165 m. At resistance level 4, if I put a weight greater than or equal to 0.750...
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